Browsing by Author "Wills, Michael Thomas"

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    Computing the trace of an endomorphism of a supersingular elliptic curve
    Wills, Michael Thomas (Virginia Tech, 2021-06-10)
    We provide an explicit algorithm for computing the trace of an endomorphism of an elliptic curve which is given by a chain of small-degree isogenies. We analyze its complexity, determining that if the length of the chain, the degree of the isogenies, and the log of the field-size are all O(n), the trace of the endomorphism can be computed in O(n⁶) bit operations. This makes explicit a theorem of Kohel which states that such a polynomial time algorithm exists. The given procedure is based on Schoof's point-counting algorithm.